Bibliography:

Options of Command by Trevor N. Dupuy
Brassey's Encyclopedia of Land Forces and Warfare by Franklin D. Margiotta
War Games by Thomas B. Allen

The Quantified Judgement Model

Outcome_Battle = Power_Red / Power_Blue

Power_Red = Numbers_Red * Variables_Red * Quality_Red

Power_Blue = Numbers_Blue * Variables_Blue * Quality_Blue

Where:

Numbers_Red/Blue = Number of Troops on each side

Variables_Red/Blue = Variables in favor of each side. Usually fortifications, prepared fighting positions, etc.

Quality_Red/Blue = Quality of troops on each side.

Obviously, this simple formula only works if both sides are essentially evenly matched with the same types of equipment and practice roughly the same types of combat formations.

You can modify the QJM further to take into account even more factors; such as mixed types of troops. You could arbitrarily declare that a tank is worth 25 men, et cetera; or modify the Law further to take into account more variables.

Modified QJM Power Calculation

Power_Blue/Red = Quantity * Quality * TLI * Effectiveness_{Fortification}

Suggested Quality Ratings for the Modified QJM:

0.1 = African Militas / Typical Science Fiction Militaries (I'm looking at you, Star Trek)
0.5 = Green Troops
1.0 = Average Troops
1.2 = Crack Troops
1.5 = Elite Troops

Computing TLI (Theoretical Lethality Index) for a semi-mobile weapon system:

TLI = ROF * Targets * Damage * Range * Accuracy * Reliability

Where:

ROF = Rate of Fire Per Minute

Targets = Targets hit with each attack. An anti-tank missile or AP round would have a Target of 1 against armor; while a High Explosive Fragmentation shell would have a Target of 10 against infantry.

Damage: Probability of destroying the target if it is hit.

Range: Effective range of the weapon in meters

Accuracy: Percentage of time the weapon actually hits it's target

Reliability: Percentage of time the weapon actually can fire.

Computing TLI (Theoretical Lethality Index) for a highly-mobile weapon system:

TLI = [ ( ROF * Targets * Damage * Range * Accuracy * Reliability * MOF * ROA) + PF ] * RFE * FCE * ASE * WHT * AME * CL

Where:

ROF = Rate of Fire Per Minute

Targets = Targets hit with each attack. An anti-tank missile or AP round would have a Target of 1 against armor; while a High Explosive Fragmentation shell would have a Target of 10 against infantry.

Damage: Probability of destroying the target if it is hit.

Range: Effective range of the weapon in meters

Accuracy: Percentage of time the weapon actually hits it's target

Reliability: Percentage of time the weapon actually can fire.

MOF: Battlefield Mobility Factor

ROA: Radius of Action Factor

PF: Punishment Factor

RFE: Rapidity of Fire Effect (Armored Vehicles Only)

FCE: Fire Control Effect (Armored Vehicles Only)

ASE: Ammunition Supply Effect (Armored Vehicles Only)

WHT: Wheels/Halftrack Effect (Armored Vehicles Only)

AME: Amphibious Capability Effect (Armored Vehicles Only)

CL: Ceiling Effect (Aircraft Only)

Computing the Battlefield Mobility Factor (MOF)

0.15 * SQRT(Speed)

Speed is measured in km/h.

Computing the Radius of Action Factor (ROA)

0.08 * SQRT(RoadRange)

Road Range is measured in kilometers.

Computing the Punishment Factor (PF)

(Weight / 2)^3/2

Weight is measured in metric tons.

Suggested Effectiveness Ratings for Fortifications for the Modified QJM:

1.0 = Attacking or Defending in the Open
1.3 = Fighting from a Hasty Position
1.5 = Fighting from a Prepared Position
1.6 = Fighting from a Fortified Position